An introductory, concise book of 220 pages on Higher Dimensional Algebra (HDA) and some elements of Homology Theory and early Algebraic Geometry (AG). Also contains some of the necessary background in Abstract Algebra, Topology, Algebraic Topology and Category Theory.

Table of Contents/Articles:
Algebra and Topology 1
Abstract algebra 1
Set (mathematics) 4
Binary operation 12
Function composition 13
Bijection 16
Associativity 18
Group (mathematics) 22
Group action 43
Field (mathematics) 49
Topology 58
Topological space 64
Vector space 69
Groupoids and Double Groupoids 92
Groupoid 92
2- groupoid 97
Double groupoid 99
Algebraic Topology 102
Crossed module 102
Fundamental groupoid 104
Seifertâvan Kampen theorem 109
Lie groupoid 113
Lie algebroid 115
Chain complex 117
Homology 119
Homology theory 123
Homological algebra 125
Group cohomology 128
Cohomology 134
Theory of Categories 138
Category theory 138
Category (mathematics) 145
Morphism 149
Isomorphism 154
Functor 158
Natural transformation 162
Categorical algebra 165
Functor category 167
Higher category theory 169
Categorical group 170
2- category 172
N- category 174
Colored graph 175
Multicategory 188
Enriched category 189
Metamathematics 192
Metatheory 192
Metalogic 193
Metamathematics 196
Alexander Grothendieck 198
Grothendieck's Programme 206
Esquisse d'un Programme 206
Grothendieck's Galois theory 210
Ronald Brown (mathematician) 211
References
Article Sources and Contributors 218

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